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<b>let </b><font color="Maroon" title="c1">O</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">G</font> be   <a href="group_9.html#NM2" title="GROUP_9:NM.2">GroupWithOperators</a> of <font color="Maroon" title="c1">O</font>;<br/><b>let </b><font color="Maroon" title="c3">H</font> be  <a href="group_9.html#V2" title="GROUP_9:attr.2">strict</a>  <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Maroon" title="c2">G</font>;<br/>





<a NAME="E1:109"/><i><font color="Green" title="E85">A1</font></i>: 
 <a href="group_9.html#K15" title="GROUP_9:func.15">carr</a> <span class="p1">(<span class="default"><a href="group_9.html#K4" title="GROUP_9:func.4">(1).</a> <font color="Maroon" title="c2">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <font color="Maroon" title="c2">G</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="group_9.html#D8" target="_self" title="GROUP_9:def.8">Def8</a></i>;<br/>
<a NAME="E2:109"/>
 <a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <font color="Maroon" title="c2">G</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c3">H</font>
 
<b>by </b><i><a class="txt" href="group_9.html#E45"><i><font color="Green" title="E41">Lm18</font></i></a></i>;<br/>
<a NAME="E3:109"/><b>then </b>
 <a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="group_9.html#K15" title="GROUP_9:func.15">carr</a> <font color="Maroon" title="c3">H</font>
 
<b>by </b><i><a class="ref" href="struct_0.html#D5" title="STRUCT_0:def.5">STRUCT_0:def 5</a></i>;<br/>
<a NAME="E4:109"/><b>then </b>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <font color="Maroon" title="c2">G</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="group_9.html#K15" title="GROUP_9:func.15">carr</a> <font color="Maroon" title="c3">H</font>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T37" title="ZFMISC_1:th.37">ZFMISC_1:37</a></i>;<br/>
<a NAME="E5:109"/><b>then </b>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <font color="Maroon" title="c2">G</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="group_9.html#K15" title="GROUP_9:func.15">carr</a> <font color="Maroon" title="c3">H</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_9.html#K15" title="GROUP_9:func.15">carr</a> <font color="Maroon" title="c3">H</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T12" title="XBOOLE_1:th.12">XBOOLE_1:12</a></i>;<br/>
<b>hence </b><a NAME="E6:109"/>
( <span class="p1">(<span class="default"><a href="group_9.html#K4" title="GROUP_9:func.4">(1).</a> <font color="Maroon" title="c2">G</font></span>)</span> <a href="group_9.html#K19" title="GROUP_9:func.19">"\/"</a> <font color="Maroon" title="c3">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">H</font> &amp; <font color="Maroon" title="c3">H</font> <a href="group_9.html#K19" title="GROUP_9:func.19">"\/"</a> <span class="p1">(<span class="default"><a href="group_9.html#K4" title="GROUP_9:func.4">(1).</a> <font color="Maroon" title="c2">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">H</font> )
 <b>by </b><i><a class="txt" href="group_9.html#E1:109"><i><font color="Green" title="E85">A1</font></i></a>, <a class="ref" href="group_9.html#T25" target="_self" title="GROUP_9:th.25">Th25</a></i>;<br/>


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